40,915 research outputs found
A Parameterized Post-Friedmann Framework for Modified Gravity
We develop a parameterized post-Friedmann (PPF) framework which describes
three regimes of modified gravity models that accelerate the expansion without
dark energy. On large scales, the evolution of scalar metric and density
perturbations must be compatible with the expansion history defined by distance
measures. On intermediate scales in the linear regime, they form a
scalar-tensor theory with a modified Poisson equation. On small scales in dark
matter halos such as our own galaxy, modifications must be suppressed in order
to satisfy stringent local tests of general relativity. We describe these
regimes with three free functions and two parameters: the relationship between
the two metric fluctuations, the large and intermediate scale relationships to
density fluctuations and the two scales of the transitions between the regimes.
We also clarify the formal equivalence of modified gravity and generalized dark
energy. The PPF description of linear fluctuation in f(R) modified action and
the Dvali-Gabadadze-Porrati braneworld models show excellent agreement with
explicit calculations. Lacking cosmological simulations of these models, our
non-linear halo-model description remains an ansatz but one that enables
well-motivated consistency tests of general relativity. The required
suppression of modifications within dark matter halos suggests that the linear
and weakly non-linear regimes are better suited for making complementary test
of general relativity than the deeply non-linear regime.Comment: 12 pages, 9 figures, additional references reflect PRD published
versio
Beyond the Standard IAU Framework
We discuss three conceivable scenarios of extension and/or modification of
the IAU relativistic resolutions on time scales and spatial coordinates beyond
the Standard IAU Framework. These scenarios include: (1) the formalism of the
monopole and dipole moment transformations of the metric tensor replacing the
scale transformations of time and space coordinates; (2) implementing the
parameterized post-Newtonian formalism with two PPN parameters - beta and
gamma; (3) embedding the post-Newtonian barycentric reference system to the
Friedman-Robertson-Walker cosmological model.Comment: 9 pages, no figures, submitted to the proceedings of the IAU 261
Symposium "Relativity in Fundamental Astronomy: Dynamics, Reference Frames,
and Data Analysis"", Virginia Beach, USA; May 200
Physics-based passivity-preserving parameterized model order reduction for PEEC circuit analysis
The decrease of integrated circuit feature size and the increase of operating frequencies require 3-D electromagnetic methods, such as the partial element equivalent circuit (PEEC) method, for the analysis and design of high-speed circuits. Very large systems of equations are often produced by 3-D electromagnetic methods, and model order reduction (MOR) methods have proven to be very effective in combating such high complexity. During the circuit synthesis of large-scale digital or analog applications, it is important to predict the response of the circuit under study as a function of design parameters such as geometrical and substrate features. Traditional MOR techniques perform order reduction only with respect to frequency, and therefore the computation of a new electromagnetic model and the corresponding reduced model are needed each time a design parameter is modified, reducing the CPU efficiency. Parameterized model order reduction (PMOR) methods become necessary to reduce large systems of equations with respect to frequency and other design parameters of the circuit, such as geometrical layout or substrate characteristics. We propose a novel PMOR technique applicable to PEEC analysis which is based on a parameterization process of matrices generated by the PEEC method and the projection subspace generated by a passivity-preserving MOR method. The proposed PMOR technique guarantees overall stability and passivity of parameterized reduced order models over a user-defined range of design parameter values. Pertinent numerical examples validate the proposed PMOR approach
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